Preheat oven to 325°F. Put a kettle of water on to heat for the water bath.

Combine 1/3 cup sugar and 1 tablespoon water in a small heavy saucepan. Bring to a simmer, stirring occasionally to dissolve the sugar. Cook over medium heat, without stirring, until the caramel turns a deep amber color, 5 to 6 minutes. Immediately divide among four 6-ounce ramekins or custard cups, tilting them to coat the bottom evenly.

Combine milk, coffee and the remaining 1/3 cup sugar in a medium saucepan. Heat over medium heat, stirring, until steaming hot but not boiling. Cover and let stand for 5 minutes. Strain through a sieve lined with cheesecloth into a bowl.

Whisk eggs and egg white in a large bowl. Slowly whisk in the hot milk mixture. Skim foam from the surface, then ladle the custard into the caramel-lined ramekins. Place the ramekins in a small roasting pan and pour enough boiling water into the pan to come halfway up the sides of the ramekins. e the custards until they appear firm when lightly shaken, about 40 minutes. Remove from the pan and let cool on a wire rack for 1 hour. Refrigerate until chilled, about 1 hour.

To serve, run a sharp knife around the inside edge of each ramekin. Set a plate upside down on a ramekin; grasping mold and plate together, quickly turn over and jerk downward several times. The crème caramel should fall onto the plate. Scrape any leftover caramel over the custard.